Probably the idea was to keep the current from crossing the heart/chest area, the right side being further away (to some extent in most people).

There's a similar rule for HV work (and when working with vacuum tube-based equipment) - "one hand in pocket"; again, the idea being that if you're working on a live system, you aren't touching things with both hands leading to a shock across the heart area.

Another rule for live systems (this applies both for higher voltages and for low voltage systems - it's mainly to protect the circuit and components):

If you have to test/measure a live system, it's best to hook up the test equipment in the "dead" state, then power up the system, then shut down before removal or changing the position of the test leads, etc.

But if this isn't possible, the next best thing to do is to hook one lead (if say using a multimeter) to a common reference point (that depends on the circuit and what you're measuring and where - but usually it's a shared ground point), and probe with the other using only one hand. Try to never probe with both hands/probes - because it can lead to inadvertent shorts and other problems. As always, there are exceptions to this rule, but they should only be considered after very careful thought and planning.

I'm generally in awe of long-lived procedures intended for mass distribution.

There's a beauty of succinct purpose.

A 14 year old with no scientific background can understand "one hand in pocket or you're dead." He or she would far less reliably understand "This is how voltage works. This is how it reacts with your body. This is how..."